Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems

  • Research Papers
  • Published:
Structural optimization Aims and scope Submit manuscript

Abstract

A standard technique for generating the Pareto set in multicriteria optimization problems is to minimize (convex) weighted sums of the different objectives for various different settings of the weights. However, it is well-known that this method succeeds in getting points from all parts of the Pareto set only when the Pareto curve is convex. This article provides a geometrical argument as to why this is the case.

Secondly, it is a frequent observation that even for convex Pareto curves, an evenly distributed set of weights fails to produce an even distribution of points from all parts of the Pareto set. This article aims to identify the mechanism behind this observation. Roughly, the weight is related to the slope of the Pareto curve in the objective space in a way such that an even spread of Pareto points actually corresponds to often very uneven distributions of weights. Several examples are provided showing assumed shapes of Pareto curves and the distribution of weights corresponding to an even spread of points on those Pareto curves.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Das, I.; Dennis, J.E. 1996: Normal-Boundary Intersection: A new method for generating Pareto-optimal points in multicriteria optimization problems.SIAM J. Optimiz. (accepted)

  • Eschenauer, H.; Koski, J.; Osyczka, A. 1990:Multicriteria design optimization. Berlin, Heidelberg, New York: Springer

    Google Scholar 

  • Jahn, J.; Klose, J.; Merkel, A. 1991: On the application of a method of reference point approximation to bicriterial optimization problems in chemical engineering. In: Oettli, W.; Pallaschke, D. (eds.)Advances in optimization, pp. 478–491. Berlin, Heidelberg, New York: Springer

    Google Scholar 

  • Koski, J. 1988: Multicriteria truss optimization. In: Stadler, W. (ed.)Multicriteria optimization in engineering and in the sciences, pp. 263–307. New York: Plenum Press

    Google Scholar 

  • Lin, J.G. 1976: Multiple-objective problems: Pareto-optimal solutions by method of proper equality constraints.IEEE Trans. Auto. Control 21, 641–650

    Google Scholar 

  • Rao, J.R.; Papalambros, P.Y. 1989: A nonlinear programming continuation strategy for one parameter design optimization problems.Proc. ASME Design Automation Conf. (held in Montreal), pp. 77–89

Download references

Author information

Authors and Affiliations

  1. Department of Computational and Applied Mathematics, Rice University of Houston, 77251-1892, TX, USA

    I. Das & J. E. Dennis

Authors
  1. I. Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. E. Dennis
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by J. Sobieski

Rights and permissions

Reprints and permissions

About this article

Cite this article

Das, I., Dennis, J.E. A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems. Structural Optimization 14, 63–69 (1997). https://doi.org/10.1007/BF01197559

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01197559

Keywords

Search

Navigation